Answer:
Explanation:
Hi!
To find the inverse, first we express your function as:
y = 3x - 8
Then, we interchange x and y variables:
x = 3y - 8
From there, we isolate y:
x + 8 = 3y
x/3 + 8/3 = y
Then, the inverse, g(x) = (x+8)/3.
We can check this by getting g(f(x)):
(f(x) + 8)/3 = (3x - 8 + 8)/3 = 3x /3 = x.
This is correct by the definition of the inverse function.
You can also think about the inverse as a "reverse function", so for example, in f(x) = 3x-8, x is multiplied by 3, then 8 is subtracted from it.
If we are to go from f(x) to x, we first add 8 (to reverse the subtraction), then divide by 3 (to reverse the multiplication).
This means g(y) = (y+8)/3, the same answer.
Hope this helps!